How to calculate the area of this?

Answer:

6 workers

Step-by-step explanation:

Number workers to earnings is direct proportion.

8: 2400 :: x : 1800

Product of means = Product of extremes

2400 * x = 8*1800

           \(x = \frac{8*1800}{2400}\\\\x=6\)

Answer:

6 workers will earn Rs. 1800.

Step-by-step explanation:

Given :-

To find :-

Solution :-

Let

no. of workers will earn Rs. 1800 = x.

We need to write a ratio to solve.

using cross products

Divide each side by 2400

Hence, 6 workers will earn Rs. 1800.

Step-by-step explanation:

\( \frac{5}{8} (4x - 16) = 20\)

\( \frac{5}{2} x - 10 = 20\)

\( \frac{5}{2}x = 20 - 10\)

\(x = 4\)

According to the given statement The probability that the sum equals Erika's age in years is 2/12, which simplifies to 1/6.

To find the probability that the sum of the numbers equals Erika's age of 14, we need to consider all possible outcomes and calculate the favorable outcomes.
First, let's consider the possible outcomes for flipping the coin. Since the coin has sides labeled 10 and 20, there are 2 possibilities: getting a 10 or getting a 20.
Next, let's consider the possible outcomes for rolling the die. Since a standard die has numbers 1 to 6, there are 6 possibilities: rolling a 1, 2, 3, 4, 5, or 6.
To find the favorable outcomes, we need to determine the combinations that would result in a sum of 14.
If Erika gets a 10 on the coin flip, she would need to roll a 4 on the die to get a sum of 14 (10 + 4 = 14).
If Erika gets a 20 on the coin flip, she would need to roll an 8 on the die to get a sum of 14 (20 + 8 = 14).
So, there are 2 favorable outcomes out of the total possible outcomes of 2 (for the coin flip) multiplied by 6 (for the die roll), which gives us 12 possible outcomes.
Therefore, the probability that the sum equals Erika's age in years is 2/12, which simplifies to 1/6.

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The scale factor was used for each dilation are-

A transformation that changes the size of a figure is called a dilatation. This indicates that the preimage as well as image are similar and have been scaled up or down, respectively.

A dilatation that results in a reduction (imagine shrinking) or an enlargement (think stretching) produces a smaller or larger image, respectively.

Part a: For ΔABC

Length AB = 2 units

Length A'B' = 4 units

A'B' = 2 *AB

Thus,  For ΔABC - scale factor = 2

Part b: For ΔDEF -

Length DF = 2 units

Length D'F' = 1  units

D'F' = 1/2 DF

Thus, For ΔDEF - scale factor = 1/2

Part c: For ΔGHJ -

Length GH = 3 units

Length G'H' = 1  units

G'H' = 1/3 GH

Thus,  For ΔGHJ - scale factor = 1/3

Part d: For ΔKML -

Length KM = 2 units

Length K'M' = 6  units

K'M' = 3*KM

Thus, For ΔKML - scale factor = 3

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Answer:

Step-by-step explanation:

f(x) = 2x³ + ax² - 7a²x - 6a³

= 2x³ - 2a²x + ax² - a³ - 5a²x - 5a³

= 2x(x² - a²) + a(x² - a²) - 5a²(x+a)

= (2x+a)(x - a)(x + a) - 5a²(x + a)

= (x + a)[(2x + a)(x - a) - 5a²]

= (x + a)(2x² - ax - 6a²)

= (x + a)(2x + 3a)(x - 2a)

x-a is the factor of the equation and x + a is not a factor of the equation,

All the roots of the equation are x + a, 2x+3a, x-2a.

"In algebra, a cubic equation in one variable is an equation of the form

ax^3+bx^2+cx+d=0

in which a is nonzero.

The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). "

Given equation is \(f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3\)

Now,

\(f(x) = 2x^3 + ax^2 - 7a^2x - 6a^3\\\\= 2x^3 - 2a^2x + ax^2 - a^3 - 5a^2x - 5a^3\\\\= 2x(x^2 - a^2) + a(x^2 - a^2) - 5a^2(x+a)\\\\= (2x+a)(x - a)(x + a) - 5a^2(x + a)\\\\= (x + a)[(2x + a)(x - a) - 5a^2]\\\\= (x + a)(2x^2 - ax - 6a^2)\\\\= (x + a)(2x + 3a)(x - 2a)\)

Hence, the roots of the equation are x + a,  2x  +3a,  x - 2a.

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Answer:

It should be ≈ 6,6

calculated the angle <CAB and both are 90°. But that would mean BC is wrong

Answer:

63/8

Step-by-step explanation:

11/8 + 13/4

= 11 + 13x4 /8

= 11 + 52/8

= 63/8

Hope it helps!!

A rational expression seems to be undefined when ever the denominator is zero.

Here given expression, 5/(x - 10)

The expression becomes undefined when denominator becomes 0.

So here, if x = 10 then the denominator becomes 0.

That is 5/10-10

= 5/0

which is undefined, when x = 10.

Given expression, 15/(y² + 4)

To a expression to be undefined denominator has to be 0.

But here denominator cannot become zero.

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Answer:

2x^2+3x^4+1

Step-by-step explanation:

a trinomial  is composed by three monomials.

So only A and B can be correct

the degree of a polynomial is the same of the monomial that compose it with the biggest degree

so the answer is B because the monomial with the biggest degree is 3x^4 (its degree is 4)

Matrix:\(A = \begin{bmatrix} 2 & 1  \\ 1 & 3   \end{bmatrix}\)

Vector\(b = \begin{bmatrix} 2 \\ 1\end{bmatrix}\)

The solution set of Ax = b is a line in the form of x = tb + s, where t and s are real numbers. This line does not contain the origin (0,0) if the vector b is not the zero vector. For example, if we take A and b as given above, then the solution set of Ax = b is x = tb + s, where t and s are real numbers, which is a line that does not contain the origin, since b is not the zero vector. To calculate, we can use the Gauss-Jordan elimination method to find the reduced row echelon form of A, which is \(matrix\begin{bmatrix} 1 & 0  \\  0 & 1 \end{bmatrix}\).Then, the solution set of Ax = b is \(x = \begin{bmatrix}2 \\ 1\end{bmatrix}\)which is a line that does not contain the origin.

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Over the course of the month, the pea plant expanded to a height of 31 inches.

It is necessary to calculate the measurements to a standard unit, such as inches or feet, in order to calculate the pea plant's growth.

For uniformity, let's convert both measurements to inches.

Given: 11 inches is the starting height.

Height at the end = 3.5 feet

3.5 feet to inches conversion:

12 inches = 1 foot.

42 inches = 3.5 feet (3.5 × 12).

Now that we have the starting height and the finishing height, we can compute the growth:

Growth = Ending height - Starting height

= 42 inches - 11 inches

= 31 inches

Therefore, the pea plant grew 31 inches in height over the course of the month.

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Answer:

(Hope this helps can I pls have brainlist (crown)☺️)

Step-by-step explanation:

Graph in pic

(Credits: Symbolab)

Answer:

where is the question

Step-by-step explanation:

0.80 = (x + 8)(0.05) is the equation used to find x.

Given,

Darryl has a solution of bleach with the concentration of 10%.

10% bleach solution means in 100 ml solution amount of bleach is 10 gm

Here,

Darryl wants to change the concentration of this solution to 5%, means he wants to add water so that amount of liquid will change but amount of bleach in grams will remain the same.

Amount of bleach in 8 gallons of 10% solution of bleach will be = (Volume)×(concentration) = 8(.10) gm

Let Darryl adds x gallons of water in 10% solution of bleach to make it 5% solution of bleach.

Amount of bleach in 5% solution of bleach = (x + 8)(0.05) gm

Now in both the concentrations of bleach solution amount of bleach will remain same.

So, 0.8 = (x + 8)(0.05) will be the equation from which he can find the value of x.

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To calculate the present value of a zero-coupon bond, we can use the formula: Present Value = Future Value / (1 + Interest Rate)^n

where Future Value is the par value of the bond, Interest Rate is the annual market interest rate, and n is the number of years. In this case, the Future Value is $2,000, the Interest Rate is 10% (or 0.10), and the number of years is 5. Using Excel, we can calculate the present value as follows:
1. In cell A1, enter the Future Value: 2000
2. In cell A2, enter the Interest Rate: 0.10
3. In cell A3, enter the number of years: 5
4. In cell A4, enter the formula for calculating the present value: =A1 / (1 + A2)^A3
5. Press Enter to get the result.

The present value of the 5-year zero-coupon bond with a $2,000 par value and an annual market interest rate of 10% is $1,620.97.

The formula for present value calculates the current worth of a future amount by discounting it back to the present using the interest rate. In this case, the future value is $2,000, and we divide it by (1 + 0.10)^5 to account for the effect of compounding over 5 years. The result is the present value of $1,620.97, which represents the amount that is considered equivalent to receiving $2,000 in 5 years at a 10% interest rate.

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Answer:

ALSO LOVE THESE

Step-by-step explanation:

Multiply 5 by what is in the parenthasees

65 + 25x

Answer:

65+25x or 25x+65

Step-by-step explanation:

The derivative of function f(x) = xlog6(1+x^2) is f'(x) = log6(1+x^2) + 2x^2/(1+x^2).

To differentiate the given function, we apply the product rule. Let u = x and v = log6(1+x^2). Then, u' = 1 and v' = (2x)/(1+x^2).

Applying the product rule formula, f'(x) = u'v + uv'. Substituting the values, we get f'(x) = 1 * log6(1+x^2) + x * (2x/(1+x^2)).

Simplifying further, f'(x) = log6(1+x^2) + 2x^2/(1+x^2).

Therefore, the derivative of f(x) = xlog6(1+x^2) is f'(x) = log6(1+x^2) + 2x^2/(1+x^2).

To differentiate the function f(x) = xlog6(1+x^2), we use the product rule. Let u = x and v = log6(1+x^2). Taking the derivatives, u' = 1 and v' = (2x)/(1+x^2).

Applying the product rule formula, f'(x) = u'v + uv'. Substituting the values, we obtain f'(x) = 1 * log6(1+x^2) + x * (2x/(1+x^2)). Simplifying further, f'(x) = log6(1+x^2) + 2x^2/(1+x^2).

Thus, the derivative of f(x) = xlog6(1+x^2) is f'(x) = log6(1+x^2) + 2x^2/(1+x^2).

This derivative represents the instantaneous rate of change of the original function at any given value of x and allows us to analyze the behavior of the function with respect to its slope and critical points.

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Answer: 699

Step-by-step explanation:

If MSwithin is smaller than MSbetween, then increasing MSwithin and/or decreasing MSbetween will lead to an increase in the F statistic.

The F statistic is calculated by dividing the variance between groups (MSbetween) by the variance within groups (MSwithin). Therefore, to increase the value of the F statistic, either the numerator (MSbetween) needs to increase, or the denominator (MSwithin) needs to decrease.

So, the answer is:

a. MSwithin > MSbetween

If the variance within groups (MSwithin) is reduced or the variance between groups (MSbetween) is increased, the F statistic will increase. Therefore, if MSwithin is smaller than MSbetween, then increasing MSwithin and/or decreasing MSbetween will lead to an increase in the F statistic.

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Answer:

-1/m^3

Step-by-step explanation:

m-3n/6m^3n - m+3n/6mn^3

=(m-3n)-(m+3n)/6m^3n  [6m^3n is the L.C.M]

=m-3n-m-3n/6m^3n

=-6n/6m^3n

= -1/m^3

   (Ans)

We can rewrite the sum as:

(9c - 8d) + (2c - 6) + (-d + 3)  =  11c - 9d - 3

So the correct option is B.

Here we want to simplify the sum:

(9c - 8d) + (2c - 6) + (-d + 3)

Grouping like terms we will get:

(9c - 8d) + (2c - 6) + (-d + 3) = (9c + 2c) + (-8d - d) + (-6 + 3)

Now we can take c and d as common factors in the first and second term to get:

(9c + 2c) + (-8d - d) + (-6 + 3)  = (9 + 2)*c + (-8 - 1)*d +  (-6 + 3)

And now simplify this to get:

(9 + 2)*c + (-8 - 1)*d +  (-6 + 3) = 11c - 9d - 3

So the correct option is B.

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Answer:

-7 1/2 equals to -7.5

so

-7.5 ___ -7.75

-7.5 > -7.75

The coefficients of the series solution for the given differential equation are:

a0 = 4, a1 = 1, a2 = -1/2, a3 = -1/12, a4 = -1/120.

To solve the given differential equation using series methods, we assume a power series solution of the form y = ∑(n=0 to ∞) anxn, where an represents the coefficients of the series. Substituting this series into the differential equation and equating the coefficients of like powers of x, we can determine the values of the coefficients.

First, we differentiate y with respect to x:

y' = a1 + 2a2x + 3a3x^2 + 4a4x^3 + ...

Next, we differentiate y' with respect to x:

y'' = 2a2 + 6a3x + 12a4x^2 + ...

Substituting these expressions for y and its derivatives into the differential equation, we get:

(-5+x)(2a2 + 6a3x + 12a4x^2 + ...) + (1-x)(a1 + 2a2x + 3a3x^2 + 4a4x^3 + ...) + (-1-5x)(a0 + a1x + a2x^2 + a3x^3 + a4x^4 + ...) = 0

Equating coefficients of like powers of x, we can solve for the coefficients one by one.

For the coefficient of x^0:

(-5)(2a2) + (1)(a1) + (-1)(a0) = 0

-10a2 + a1 - a0 = 0

For the coefficient of x^1:

(-5)(6a3) + (1)(2a2) + (-1)(a1) + (-5)(a0) = 0

-30a3 + 2a2 - a1 - 5a0 = 0

For the coefficient of x^2:

(-5)(12a4) + (1)(3a3) + (-1)(a2) + (-5)(a1) = 0

-60a4 + 3a3 - a2 - 5a1 = 0

For the coefficient of x^3:

(-5)(0) + (1)(4a4) + (-1)(a3) + (-5)(a2) = 0

4a4 - a3 - 5a2 = 0

For the coefficient of x^4:

(-5)(0) + (1)(0) + (-1)(a4) + (-5)(a3) = 0

-6a3 + a4 = 0

Using the initial conditions y(0) = 4 and y'(0) = 1, we can substitute these values into the equations above to determine the coefficients.

Solving the system of equations, we find:

a0 = 4, a1 = 1, a2 = -1/2, a3 = -1/12, a4 = -1/120.

The coefficients of the series solution for the given differential equation are a0 = 4, a1 = 1, a2 = -1/2, a3 = -1/12, and a4 = -1/120. These coefficients can be used to form the series solution of the differential equation: y = 4 + x - (1/2)x^2 - (1/12)x^3 - (1/120)x^4 +)

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Hey there! :)

Answer:

(2, 3) and (-2, 11).

Step-by-step explanation:

To solve this system of equations, we can set both equations equal to each other:

x² -2x + 3 = -2x + 7

Combine like terms:

x² -4 = 0

Factor using difference of squares:

(x - 2)(x + 2) = 0

Therefore, x = 2 and -2. Plug both of these into an equation to solve for the 'y' value:

f(x) = -2(2) + 7

f(x) = -4 + 7

f(x) = 3

------------------

f(x) = -2(-2) + 7

f(x) = 4 + 7

f(x) = 11

Therefore, the two ordered pairs are (2, 3) and (-2, 11).

Step-by-step explanation:

JKL is congruent to ABC

side LK corresponds to WV and CB

angle JLK corresponds to angle UWV and angle ACB

Looking at the graph

the solution is the interval [-6,6]

the mean is 0

Answer:

=================

Use the intersecting chords theorem, according to which, the products of the lengths of the line segments on each chord are equal,

or

Substitute the lengths and solve for x:

The matching answer choice is A.

If the length is Fraction 2 over 3 unit and the width is Fraction 1 over 3 unit The perimeter of the rectangle is 2 units.

First, substitute l = 2/3 and w = 1/3 in the expression for the perimeter of the rectangle:

P = 2(l + w)

P = 2(2/3 + 1/3)

P = 2(1)

P = 2

A rectangle is a four-sided flat shape with four right angles. It is a type of quadrilateral, which means it has four sides.

The perimeter of a rectangle is the total distance around the outside of the rectangle. It is calculated by adding up the length of all four sides of the rectangle. The formula for the perimeter of a rectangle is:

Perimeter = 2(length + width)

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Answer:-

\(\frac{1}{3}\)

Step-by-step explanation:

Delta y / Delta x (delta = difference of)

\(\frac{1}{3}\).